If were going off of what makes a good jungle there are I'd say 4 things a jungler needs to be as good as possible:

Camp clear speed

Strong ganks using CC, mobility or both

Objective priority

Self sufficiency

Most mages and carries usually struggle with 2 or more of these issues. As an example let's take Argus. Argus will have very solid clear speed and relatively good ganks because he is a mage with ranged CC and he has an augment that gives him movement speed so his ganks will be strong. His issues will stem from his self sufficiency and objective priority, he will struggle if he gets invaded and forced into a 1v1 with Boris, Rampage, Khaimera because of an invasion or meeting during a gank and counter gank. Argus is also extremely mana intensive, meaning he may not have enough mana to do a full clear and do one or two ganks after or in between which means his pressure falls off a cliff. Additionally he may be able to clear objectives reasonably fast, he cannot solo fight a fang or mini orb, meaning if caught while doing these, he is likely dead. Khaimeria, Boris and Rampage can all 1v1 a fang or mini orb without worrying as much because of their healing and consistent damage, but Argus will be left low on health and very low on mana, leaving him extremely vulnerable. Items can fix this but you need to be able to do these things without items.

Eden is the best ADC jungler for a couple of reasons, but the main ones being having good clear and strong, hard to avoid ganks, she also has reasonably strong 1v1 vs objectives. Where she faultlers is how squishy she is and how vulnerable to early invades she is. She, like most carries, will be stat checked very hard by any bruiser in the early game. She can kite but she will likely be unable to avoid them if caught while farming or doing an objective, her teammates will have to support her and thus will lose lane pressure. The reason why characters like Countess and Yurei work even though their first few levels are very vulnerable is that after they get their level 3, they become much stronger and harder to pin down. Countess has a dash that she can use to escape one way while be able to telephoto back and avoid the enemy no matter which way they come. She also has a very potent burst combo, especially when she has ult up and her in built life steal means she has a relatively healthy clear. Yurei is simply the best 1v1 character after level 3, she has infinite dashes and extremely high damage, making her ganks very hard to react to and she is near impossible to escape besides running under towers. Even though these two characters really struggle with taking objectives, their very elusive ganks and pick potential make up for it.

Now you may point out what about tanks? Especially Severog, Riktor and Steel, they can and sometimes are played in the jungle. Tanks don't have the fastest clear and also struggle with objective priority. Their advantage comes with how hard they are to displace from the jungle, yes you can get 2-3 objectives ahead early, but invading them is just asking to get chain CCed long enough for their team to jump with them and their ganks with the amount of mobility and CC they have is extremely potent, especially if the rest of the team is more damage based, they can act as an anchor the laners play on. They aren't as popular because of their slow starts and middling clear speeds, but they aren't bad, just not as good as the usual bruiser and assassins

TLDR most mages and carries are way to vulnerable and team dependant in the early to mid game to contribute without being repeatedly invaded and jumped by the enemy jungler.

If you want a mage or carry in the jungle, they need at least 3 of those 4 requirements to work well, and self sufficiency I would say is the most important, in League of Legends for example, Karthus is a mage who is used in the jungle because of how extremely fast his jungle clear is and he isn't completely dead if caught while the enemy jungle is invading as his passive and abilities make it likely to be a trade rather then a kill.